where \(\xi ^a\)  is a global time like Killing vector. The exponent
\(e^\phi \)  represents the redshift factor that relates the local
time coordinate to that at a reference point with \(\phi =0\) , which
we will take to be at infinity. We choose the holographic screen
\(S\)  as a closed equipotential surface or in other words, a closed
surface of constant redshit \(\phi \) . Therefore Eq. (REF )
may be written as [1]}
\(T=\frac{\hbar }{2 \pi }e^\phi N^a \nabla _a \phi ,\) 
